Plasma-free anisotropic selective-area etching of β-Ga2O3 using forming gas under atmospheric pressure

ABSTRACT We demonstrate a facile and safe anisotropic gas etching technique for β-Ga2O3 under atmospheric pressure using forming gas, a H2/N2 gas mixture containing 3.96 vol% H2. This etching gas, being neither explosive nor toxic, can be safely exhausted into the atmosphere, simplifying the etching system setup. Thermodynamic calculations confirm the viability of gas-phase etching above 676°C without the formation of Ga droplets. Experimental verification was achieved by etching (1ˉ02) β-Ga2O3 substrates within a temperature range of 700–950°C. Moreover, selective-area etching using this method yielded trenches and fins with vertical and flat sidewalls, defined by (100) facets with the lowest surface energy density, demonstrating significant anisotropic etching capability.


Introduction
In the past decade, β-Ga 2 O 3 has emerged as a material of significant interest in power electronic devices owing to its ultrawide bandgap and high breakdown voltage, surpassing those of SiC and GaN [1].These attributes render β-Ga 2 O 3 suitable for use in highpower transistors and rectifiers.However, the successful integration of β-Ga 2 O 3 into semiconductor devices requires precise control of surface characteristics, such as doping concentrations and microstructures.The electron carrier density in β-Ga 2 O 3 can vary from 10 16 to 10 20 cm −3 through intentional impurity doping during epitaxy [2] or ion-implantation techniques [3].Achieving room-temperature p-type conductivity remains challenging because of the deep acceptor levels of potential dopants [4,5] and the expected heavy hole mass owing to the nearly flat dispersion at the upper end of the valance band [6], limiting the ability to enhance the withstand voltage of β-Ga 2 O 3 power devices while maintaining low on-resistance.For example, mesa-terminated Ni-contact Schottky barrier diodes (SBDs) have shown a maximum practical reverse electric field of 3.4 MV cm −1 , which is significantly lower than the predicted intrinsic breakdown electric field of 6-8 MV cm −1 owing to Schottky barrier tunneling, as described by the field emission model [7].However, adopting trench metal-oxidesemiconductor (MOS) structures on the surface can mitigate leakage currents in trench SBDs because the current paths are effectively depleted from their sidewalls under reverse bias, thereby enhancing the breakdown voltage [8].This approach also applies to fin-field-effect transistors (FinFETs), where gate MOS structures between fin sidewalls can enable a normally off operation, and increase breakdown voltage without needing pn homojunctions [9].Consequently, microfabrication is crucial for improving the performance of β-Ga 2 O 3 -based unipolar devices.
Plasma-based dry etching, a common microfabrication technique, can create the aforementioned trenches and fins [10].Despite its effectiveness, plasma etching can damage the material surface, or increase defects that function as trap states [11], compromising device performance, as evidenced by the increased onresistances in trench SBDs [12] and degraded effective channel mobilities and transfer characteristics with large hysteresis in FinFETs [13,14].Therefore, researchers are increasingly interested in exploring alternative etching methodologies for circumventing plasma-induced damage.
Non-plasma etching is a distinctive method for patterning and shaping the β-Ga 2 O 3 surface, preserving the surface quality of the material.Wet etching techniques, such as hot phosphoric acid etching [15] and metal-assisted chemical etching (MacEtch) [16,17], can produce microstructures with damagefree sidewalls.However, these sidewalls are positively tapered, rendering them less suitable for device integration.In contrast, plasma-free dry etching methods include Ga-flux etching [18,19], hydrogen environment anisotropic thermal etching (HEATE) [20,21], and HCl gas etching [22][23][24][25].These methods enable the creation of high-aspect-ratio structures with vertical sidewalls devoid of plasma damage, facilitated by directional Ga-beam flux or the manifestation of specific facet planes with low surface energy densities, such as (100), ( � 101), {310} facets [26][27][28].Nonetheless, these techniques require vacuum equipment and/or gas safety systems, increasing costs and limiting their widespread use.
We overcame these limitations by investigating forming gas as an etching medium under atmospheric pressure, avoiding the need for flammable or toxic gases.Forming gas comprises an inert gas (N 2 or Ar) mixed with H 2 and contains a low H 2 volume of 5% or less, classifying it as nonflammable because of its concentration being close to the lower explosive limit in air (4.0 vol%).This mixture is widely used across various fields for diverse purposes [29][30][31].In the context of β-Ga 2 O 3 device processing, forming-gas treatment at 250°C reduces the interface state density at Al 2 O 3 /β-Ga 2 O 3 interfaces [32].However, the patterning of β-Ga 2 O 3 using forming-gas etching is yet to be reported.
This study demonstrates the effectiveness of selective-area forming-gas etching on β-Ga 2 O 3 substrates.Thermodynamic calculations were employed to establish the process temperature range.Systematic etching experiments were conducted to explore the etching rate and in-plane anisotropy, which were found to depend on the process temperature.The resulting trenches and fins aligned along specific window directions featured vertical and planar sidewalls, making them suitable for device applications.

Thermodynamic analysis
Before the etching experiments, we assessed the thermal and chemical stabilities of β-Ga 2 O 3 in the presence of H 2 gas through thermodynamic analysis to determine an appropriate process window.The equilibrium partial pressures of potential gaseous species (Ga 2 O, GaO, Ga, O 2 , H 2 , H 2 O, GaH, GaH 2 , GaH 3 , and GaOH) involved in chemical reactions above the β-Ga 2 O 3 surface, along with inert N 2 , were calculated following methodologies reported in the literature [33,34].Figures 1(a,b) depict the pressure curves in N 2 -diluted H 2 (4.0 vol%) flow and pure H 2 flow under atmospheric pressure, respectively, as a function of temperature.In both scenarios, the partial pressures of Ga 2 O and H 2 O gases exceed those of other Ga-and O-containing gas species within the examined temperature range, indicating that H 2 etching predominantly occurs through the formation and desorption of Ga 2 O and H 2 O gases.Focusing on the calculated partial pressure of Ga gas (P Ga ) and the literaturereported vapor pressure of pure Ga metal (P V Ga ) [35], the two values intersect (P Ga = P V Ga ) at threshold temperatures (T X ) of 676°C for N 2 -diluted H 2 and 922°C for pure H 2 .Note that the N 2 dilution reduces the etching rate due to the lower input H 2 partial pressure, reducing P Ga and T X .T X is a pivotal parameter for H 2 etching, delineating the temperature regions where Ga droplets form (P Ga > P V Ga ) below T X , and where Ga metal is completely evaporated ðP Ga < P V Ga ) above T X .Consequently, vapor-phase etching should be conducted above T X , with N 2 dilution serving to lower T X .Based on these thermodynamic considerations, we established the process temperature range between 700°C and 950°C (above T X ) to prevent Ga droplet formation.

Experimental methods
This study employed β-Ga 2 O 3 substrates with a ( � 102) orientation, supplied by Novel Crystal Technology, Inc.The ( � 102) plane is parallel to the [010] axis and perpendicular to the (100) plane, which is known for its lowest surface energy density [26].This orientation coincides with the primary dislocation and void/nanopipe directions within the crystal [36][37][38], making it particularly suitable for vertical anisotropic etching.This avoids undesired crystal defects on the surface, favoring vertical trench and fin device applications [25].For detailed methodologies and findings from our previous experiments on ( � 102) substrates, including HCl gas etching, readers are referred to our published studies [25,39,40].
The experimental setup began with the preparation of a patterned SiO 2 mask on Sn-doped ( � 102) β-Ga 2 O 3 substrates with an effective donor concentration of ~4.9 × 10 18 cm −3 .A 0.1-μm-thick SiO 2 layer was deposited onto the substrate surface using highthroughput plasma-assisted chemical vapor deposition.Although the plasma deposition process might damage the β-Ga 2 O 3 surface, this damage should be independent of the forming-gas etching characteristics, which are the focus of this study.For practical applications, SiO 2 layers should be deposited using non-plasma techniques, such as atomic layer deposition using O 3 as an oxidant.The deposited SiO 2 layer was patterned through standard laser lithography and buffered HF etching to create masks with various window shapes.These included square, circular, radial-line windows, and two types of striped windows (Pattern T and Pattern F), designed to explore different etched structures.The dimensions for the square windows were 100 × 100 μm 2 , the circular windows had a diameter of 1.5 μm, and the radial-line windows were 1.2 μm wide.The striped windows, intended for trench and fin fabrication, had window/mask widths of 1.2/1.8μm for Pattern T and 5.5/0.7 μm for Pattern F, respectively.See Figure S1 in the supplementary file for diagrams of these window shapes.
Etching was performed in a horizontal quartz furnace equipped with a gas flow system, as illustrated in Figure 2. The substrate was heated to target temperatures of 700°C, 750°C, 800°C, 875°C, and 950°C under a 1.000 slm flow of inert N 2 gas.The temperature was monitored by a thermocouple (TC) inside the quartz tube, calibrated against a reference thermocouple placed at the sample location prior to experimentation.The etching commenced upon switching the gas supply from pure N 2 to forming gas -a mixture of H 2 and N 2 with 3.96 vol% H 2 -while maintaining a 1.000 slm flow rate.The exhaust was vented directly into the atmosphere.The process is concluded by reverting the gas supply to pure N 2 and allowing the furnace to cool to ambient temperature.This entire procedure was conducted at atmospheric pressure (~1 atm), distinguishing it from other vapor-phase etching methods by obviating the need for vacuum systems and gas safety mechanisms, thereby reducing costs.
Post-etching analyses involved measuring the depth within the square windows (100 × 100 μm 2 ) Figure 1.Equilibrium partial pressures of gaseous species above β-Ga 2 O 3 in (a) N 2 -diluted H 2 gas flow with 4.0 vol% H 2 and (b) undiluted H 2 gas flow under 1 atm as functions of temperature.Red solid lines represent the partial pressures of gaseous species, while the vapor pressure of pure Ga metal (P V Ga ) is shown with blue dashed lines.The green dotted line T X indicates the temperature at which the partial pressure of Ga (P Ga ) equals P V Ga .
Figure 2. Schematic of the forming-gas etching system utilized in this research.
using a stylus profiler and atomic force microscopy to determine the etching rate.The etched structures were then examined with scanning electron microscopy (SEM), setting the acceleration voltage to 10 kV to clearly delineate the etched hole edges without mask removal [22].Cross-sectional views of the etched structures were revealed by focused ion beam milling and further observed via SEM.

Experimental results and discussion
Etching rate of the ( � 102) surface Initially, we measured the etching rate of the ( � 102) surface across a temperature range of 700°C-950°C.Notably, no Ga droplets were detected on the etched surfaces of any samples, consistent with predictions from thermodynamic analyses.The etching rate showed a pronounced increase with elevated process temperatures.They were 6.7 ± 0.1 nm/min at 700°C, 23.4 ± 0.4 nm/min at 750°C, 51.6 ± 4.2 nm/min at 800°C, 107.1 ± 12.0 nm/min at 875°C, and 206.3 ± 12.8 nm/min at 950°C (Figure 3).This result indicates a significant enhancement of the etching reaction by thermal energy within this temperature range.To elucidate the trends associated with the process temperature, we compare structures etched at 750°C for 60 min and at 950°C for 5 min in the subsequent sections.

In-plane etching characteristics
We further explored the in-plane etching behavior by examining the side-etched shapes from a surfacenormal perspective.The etched shapes reflected the asymmetry of the β-Ga 2 O 3 crystal structure, which has two symmetry elements: two-fold rotation symmetry around the [010] axis and mirror symmetry across the (010) plane.Figure 4 summarizes the etched structures beneath circular and radial-line windows at process temperatures of 750°C and 950°C.In all the images, side-etched shapes are symmetrical in the [010] and [0 � 10] directions, reflecting the mirror symmetry across the (010) plane.
At 750°C, the etched structures reflected the in-plane anisotropy of the crystal.Figure 4(a1) shows a top-view SEM image of an etched hole beneath a circular window, where the contour of the etched shape forms a hexagon elongated along the [010] direction.This shape points to the emergence of (100)-and {310}faceted sidewalls, similar to findings from our previous HCl gas etching study on ( � 102) substrates [25].The (100) plane has the lowest surface energy density [26], while {310} planes, being oxygen-close-packing planes, are expected to have relatively low surface energy densities [28].The detailed in-plane dependence of the side-etching rate, derived from the SEM image of radial-line windows (Figure 4(a2)), is represented in polar coordinates (Figure 4(a3)).The polar plot reveals deep and shallow dips corresponding to (100) and {310} sidewalls, respectively, aligning with the elongated hexagonal shape observed under the circular window Figure 4(a1).Conversely, broad peaks around the <010> direction indicate an increased side-etching rate of the (010) plane.
At 950°C, except for the (100) facets, the sidewalls of the etched structures appeared roughened.Figure 4(b1) illustrates the etched depression under a circular window, where the contour in the <201> directions appears linear, delineated by (100) facets, while significant roughness is evident in the <010> directions.Moreover, side-etching on the [201] side surpassed that on the [ � 20 � 1] side.This structure suggests the absence of {310} sidewalls due to enhanced sideetching on the (010) plane at the elevated process temperature.Note that the asymmetry of the side-etching structures between the [ � 20 � 1] and [201] direction sides is attributed to the two-fold rotation symmetry, where the crystal lattices on the [ � 20 � 1] and [201] direction sides are rotated 180° around the [010] axis with respect to each other.Given that the etching beneath the mask proceeded not only in a lateral direction but also in a downward direction, it is likely that different crystal planes were etched between the [ � 20 � 1] and [201] direction sides owing to the asymmetric lattice structure, resulting in a marked difference in the side-etching structures.Figures 4(b2) and 4(b3) display etched trenches under radial-line windows and a polar plot of their side-etching rates, respectively.Trenches along <010> directions showed minimal side-etching rates due to (100)-faceted sidewalls, while side-etching rates increased for trenches deviating from <010> directions.Additionally, trench sidewalls near the [201] direction exhibited a zigzag pattern.A distinct butterfly-wing-like pattern in the polar plot aligns well with the etched structure observed under the circular window.Notably, the polar plot at 750°C did not show a significant difference in side-etching rates between the [201] and [ � 20 � 1] directions owing to the existence of relatively stable {310} sidewalls.These results indicate that higher process temperatures alter the etching behavior, including in-plane etching anisotropy, while (100) facets remain unaffected.

Etched trenches and fins
We further examined the structures of trenches and fins with (100)-faceted sidewalls to evaluate the potential of forming-gas etching for semiconductor processing.Figure 5 illustrates the etched structures beneath striped windows (Patterns T and F) at process temperatures of 750°C and 950°C.
The trenches and fins were successfully created in accordance with the design of the windows and masks.Surface SEM images showed minimal side-etching perpendicular to the [010] direction windows, less than 0.2 μm, regardless of the process temperature and window patterns, attributed to the formation of (100)-faceted sidewalls Figures 5(a1), 5(a4), 5(b1), and 5(b4)).This precision in patterning trenches and fins, with their widths defined accurately by the windows and masks, is advantageous for semiconductor device fabrication.Furthermore, the (100) sidewalls were observed to be perfectly flat (Figures 5(a2), 5(a5), 5 (b2), and 5(b5)), a characteristic beneficial for device applications due to the implied low surface state density on these sidewalls.However, the bottom surface of the etched areas showed relative roughness, which increased with the process temperature (Figures 5 (a4),5(a5), 5(b4), and 5(b5)).Such surface roughness is consistent with observations from HCl gas etching on ( � 102) substrates [25], suggesting that roughening is a typical result of gas etching on the ( � 102) plane.The observed roughening of the ( � 102) bottom surfaces relative to the (100) sidewall surfaces at elevated temperatures can be attributed to the difference in the roughening transition temperatures associated with the free energies of steps on the respective planes.On the ( � 102) bottom plane, the step sidewalls are predominantly formed with (100) facets (Figure 5).Since the (100) facet has the lowest surface energy density, the free energies of the steps with (100) sidewall facets on the ( � 102) bottom plane are relatively low, decreasing the roughening transition temperature.Conversely, on the (100) sidewall plane, the free energies of steps must be larger because the step sidewalls comprise facets other than the (100) facets, leading to a higher roughening transition temperature than that on the ( � 102) plane.
Cross-sectional analysis highlighted the contours of these trenches and fins.The (100) sidewalls on both sides were perfectly vertical (Figures 5(a3), 5(a6), 5(b3), and 5(b6)), demonstrating effective anisotropic etching.Notably, the profiles from the 750°C etching, with smoother bottoms, were nearly ideal.The asymmetry of the etched trenches and fins between the [ � 20 � 1] and [201] directional sides was also observed, particularly at the 950°C etching.This result is consistent with the in-plane etching characteristics discussed in the previous section.The aspect ratio of vertical anisotropy, defined as the height of the (100) sidewall divided by the side-etched length, varied from 7.0 to 8.4 at 750°C and from 13 to 30 at 950°C.These values surpass the aspect ratios of 2.7 to 6.7 reported for HCl gas etching on ( � 102) substrates at 1038°C [25].The capability of achieving vertical etching with smooth sidewall profiles highlights the potential of forming-gas etching as a viable plasma-free anisotropic dry etching technique.

Summary
We introduced a novel plasma-free anisotropic etching technique for ( � 102) β-Ga 2 O 3 substrates utilizing forming gas (a N 2 /H 2 mixture containing 3.96% H 2 ) at atmospheric pressure.Vapor-phase etching without the formation of Ga droplets was achieved at process temperatures of 700°C and above, aligning with thermodynamic predictions.The etched structures demonstrated anisotropic features reflective of the β-Ga 2 O 3 crystal structure, with side-etching minimized along the <010> direction due to the formation of (100) faceted sidewalls.This facilitated precise patterning and the creation of high-aspect-ratio trenches and fins with vertical and smooth sidewalls, devoid of plasma-induced damage.The use of forming gas simplifies the etching process, leveraging the nontoxic and nonflammable properties of the gas.This method is expected to gain traction within the β-Ga 2 O 3 research community.